A Logical Analysis of Graphical Consistency Proofs

Abstract

In this paper, we investigate the semantic mechanism of graphical consistency proofs, where one expresses a certain condition in a chart, a diagram, or some other graphical representation, and uses the existence of such an graphic as a proof of the consistency of the expressed conditions. We first show that such a proof is guaranteed to be sound by a special matching of constraints between representations and represented situations. We then extend our analysis to another types of graphics-based inferences called ``free rides{''}, and show that they also rely on a matching of constraints between representations and represented situations. Comparisons of graphical consistency proofs and free rides let us see three commonalities between these two inferential procedures, and let us define the general notion of physical on-site inference, where perceptually present objects are used as inferential surrogates through physical operations. Our analysis is therefore a clarification of the exact semantic requirements for one representative way in which a visual representation participates in distributed cognition {[}Giere, 2001] or manipulative inferences {[}Magnani, 2001].